Determination of resonant frequency and quality factor for a sensor system

ABSTRACT

A method for determining sensor parameters of an actively-driven sensor system may include obtaining as few as three samples of a measured physical quantity versus frequency for the actively-driven sensor system, performing a refinement operation to provide a refined version of the sensor parameters based on the as few as three samples and based on a linear model of an asymmetry between slopes of the measured physical quantity versus frequency between pairs of the as few as three samples, iteratively repeating the refinement operation until the difference between successive refined versions of the sensor parameters is below a defined threshold, and outputting the refined sensor parameters as updated sensor parameters for the actively-driven sensor system.

RELATED APPLICATIONS

The present disclosure claims priority to U.S. Provisional PatentApplication Ser. No. 63/044,065, filed Jun. 25, 2020, and U.S.Provisional Patent Application Ser. No. 63/086,721, filed Oct. 2, 2020,both of which are incorporated by reference herein in their entireties.The present disclosure also relates to U.S. patent application Ser. No.16/267,079, filed Feb. 4, 2019, U.S. patent application Ser. No.16/422,543, filed May 24, 2019, U.S. patent application Ser. No.16/866,175, filed May 4, 2020, and U.S. patent application Ser. No.17/079,709, filed Oct. 26, 2020, all of which are incorporated byreference herein in their entireties.

FIELD OF DISCLOSURE

The present disclosure relates in general to electronic devices withuser interfaces (e.g., mobile devices, game controllers, instrumentpanels, etc.), and more particularly, an integrated haptic system foruse in a system for mechanical button replacement in a mobile device,for use in haptic feedback for capacitive sensors, and/or other suitableapplications.

BACKGROUND

Many traditional mobile devices (e.g., mobile phones, personal digitalassistants, video game controllers, etc.) include mechanical buttons toallow for interaction between a user of a mobile device and the mobiledevice itself. However, such mechanical buttons are susceptible toaging, wear, and tear that may reduce the useful life of a mobile deviceand/or may require significant repair if malfunction occurs. Also, thepresence of mechanical buttons may render it difficult to manufacturemobile devices to be waterproof. Accordingly, mobile devicemanufacturers are increasingly looking to equip mobile devices withvirtual buttons that act as a human-machine interface allowing forinteraction between a user of a mobile device and the mobile deviceitself. Similarly, mobile device manufacturers are increasingly lookingto equip mobile devices with other virtual interface areas (e.g., avirtual slider, interface areas of a body of the mobile device otherthan a touch screen, etc.). Ideally, for best user experience, suchvirtual interface areas should look and feel to a user as if amechanical button or other mechanical interface were present instead ofa virtual button or virtual interface area.

Presently, linear resonant actuators (LRAs) and other vibrationalactuators (e.g., rotational actuators, vibrating motors, etc.) areincreasingly being used in mobile devices to generate vibrationalfeedback in response to user interaction with human-machine interfacesof such devices. Typically, a sensor (traditionally a force or pressuresensor) detects user interaction with the device (e.g., a finger presson a virtual button of the device) and in response thereto, the linearresonant actuator may vibrate to provide feedback to the user. Forexample, a linear resonant actuator may vibrate in response to userinteraction with the human-machine interface to mimic to the user thefeel of a mechanical button click.

However, there is a need in the industry for sensors to detect userinteraction with a human-machine interface, wherein such sensors provideacceptable levels of sensor sensitivity, power consumption, and size.For example, in an actively driven sensor system, it may be desirablethat a signal driver generate a driving signal at or near a resonantfrequency of the sensor. Due to manufacturing designs and tolerances aswell as environmental effects (such as temperature, humidity, movementsin air gap over time), the resonant frequency of the sensor as well asthe Q-factor of the sensor may be different for each individual sensorand can change over time. Thus, to ensure generation of a driving signalat or near such resonant frequency, it may further be desirable todetermine such resonant frequency and/or a quality factor of a sensor.

SUMMARY

In accordance with the teachings of the present disclosure, thedisadvantages and problems associated with use of a virtual button in amobile device may be reduced or eliminated.

In accordance with embodiments of the present disclosure, a method fordetermining sensor parameters of an actively-driven sensor system mayinclude obtaining as few as three samples of a measured physicalquantity versus frequency for the actively-driven sensor system,performing a refinement operation to provide a refined version of thesensor parameters based on the as few as three samples and based on alinear model of an asymmetry between slopes of the measured physicalquantity versus frequency between pairs of the as few as three samples,iteratively repeating the refinement operation until the differencebetween successive refined versions of the sensor parameters is below adefined threshold, and outputting the refined sensor parameters asupdated sensor parameters for the actively-driven sensor system.

In accordance with embodiments of the present disclosure, a system mayinclude an actively-driven sensor and a measurement circuitcommunicatively coupled to the actively-driven sensor and configured toobtain as few as three samples of a measured physical quantity versusfrequency for the actively-driven sensor system, perform a refinementoperation to provide a refined version of the sensor parameters based onthe as few as three samples and based on a linear model of an asymmetrybetween slopes of the measured physical quantity versus frequencybetween pairs of the as few as three samples, iteratively repeat therefinement operation until the difference between successive refinedversions of the sensor parameters is below a defined threshold, andoutput the refined sensor parameters as updated sensor parameters forthe actively-driven sensor system.

Technical advantages of the present disclosure may be readily apparentto one having ordinary skill in the art from the figures, descriptionand claims included herein. The objects and advantages of theembodiments will be realized and achieved at least by the elements,features, and combinations particularly pointed out in the claims.

It is to be understood that both the foregoing general description andthe following detailed description are examples and explanatory and arenot restrictive of the claims set forth in this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present embodiments and advantagesthereof may be acquired by referring to the following description takenin conjunction with the accompanying drawings, in which like referencenumbers indicate like features, and wherein:

FIG. 1 illustrates a block diagram of selected components of an examplemobile device, in accordance with embodiments of the present disclosure;

FIG. 2 illustrates a block diagram of selected components of an exampleintegrated haptic system, in accordance with embodiments of the presentdisclosure;

FIG. 3A illustrates a mechanical member separated by a distance from aninductive coil, in accordance with embodiments of the presentdisclosure;

FIG. 3B illustrates selected components of an inductive sensing systemthat may be implemented by a resonant phase sensing system, inaccordance with embodiments of the present disclosure;

FIG. 4 illustrates a diagram of selected components of an example systemfor performing resonant phase sensing, in accordance with embodiments ofthe present disclosure;

FIG. 5 illustrates an example graph of amplitude versus frequency for aresistive-inductive-capacitive sensor, in accordance with embodiments ofthe present disclosure;

FIGS. 6A-6C illustrate additional example graphs of amplitude versusfrequency for a resistive-inductive-capacitive sensor in differentpossible amplitude response regions, in accordance with embodiments ofthe present disclosure;

FIG. 7 illustrates an example graph of a sum of slopes versus a qualityfactor for a single resonant frequency of aresistive-inductive-capacitive sensor, in accordance with embodiments ofthe present disclosure;

FIG. 8 illustrates an example graph of a linear model of a product of aquality factor of a resistive-inductive-capacitive sensor multiplied bya quantity of a sum of slopes determined from sampled measurement pointsof amplitude versus frequency, in accordance with embodiments of thepresent disclosure;

FIG. 9 illustrates an example graph of amplitude versus frequency for aresistive-inductive-capacitive sensor with measurement samples takenbelow an actual resonant frequency, in accordance with embodiments ofthe present disclosure;

FIG. 10 illustrates an example graph of amplitude versus frequencydepicting an approach for determining update measurement samplingfrequencies, in accordance with embodiments of the present disclosure;

FIG. 11 illustrates an example graph of amplitude versus frequency for aresistive-inductive-capacitive sensor with measurement samples takenabove an actual resonant frequency, in accordance with embodiments ofthe present disclosure; and

FIG. 12 illustrates an example graph of amplitude versus frequencydepicting an approach for determining update measurement samplingfrequencies, in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

FIG. 1 illustrates a block diagram of selected components of an examplemobile device 102, in accordance with embodiments of the presentdisclosure. As shown in FIG. 1, mobile device 102 may comprise anenclosure 101, a controller 103, a memory 104, a force sensor 105, amicrophone 106, a linear resonant actuator 107, a radiotransmitter/receiver 108, a speaker 110, an integrated haptic system112, and a resonant phase sensing system 113.

Enclosure 101 may comprise any suitable housing, casing, or otherenclosure for housing the various components of mobile device 102.Enclosure 101 may be constructed from plastic, metal, and/or any othersuitable materials. In addition, enclosure 101 may be adapted (e.g.,sized and shaped) such that mobile device 102 is readily transported ona person of a user of mobile device 102. Accordingly, mobile device 102may include but is not limited to a smart phone, a tablet computingdevice, a handheld computing device, a personal digital assistant, anotebook computer, a video game controller, or any other device that maybe readily transported on a person of a user of mobile device 102.

Controller 103 may be housed within enclosure 101 and may include anysystem, device, or apparatus configured to interpret and/or executeprogram instructions and/or process data, and may include, withoutlimitation a microprocessor, microcontroller, digital signal processor(DSP), application specific integrated circuit (ASIC), or any otherdigital or analog circuitry configured to interpret and/or executeprogram instructions and/or process data. In some embodiments,controller 103 interprets and/or executes program instructions and/orprocesses data stored in memory 104 and/or other computer-readable mediaaccessible to controller 103.

Memory 104 may be housed within enclosure 101, may be communicativelycoupled to controller 103, and may include any system, device, orapparatus configured to retain program instructions and/or data for aperiod of time (e.g., computer-readable media). Memory 104 may includerandom access memory (RAM), electrically erasable programmable read-onlymemory (EEPROM), a Personal Computer Memory Card InternationalAssociation (PCMCIA) card, flash memory, magnetic storage, opto-magneticstorage, or any suitable selection and/or array of volatile ornon-volatile memory that retains data after power to mobile device 102is turned off.

Microphone 106 may be housed at least partially within enclosure 101,may be communicatively coupled to controller 103, and may comprise anysystem, device, or apparatus configured to convert sound incident atmicrophone 106 to an electrical signal that may be processed bycontroller 103, wherein such sound is converted to an electrical signalusing a diaphragm or membrane having an electrical capacitance thatvaries as based on sonic vibrations received at the diaphragm ormembrane. Microphone 106 may include an electrostatic microphone, acondenser microphone, an electret microphone, a microelectromechanicalsystems (MEMs) microphone, or any other suitable capacitive microphone.

Radio transmitter/receiver 108 may be housed within enclosure 101, maybe communicatively coupled to controller 103, and may include anysystem, device, or apparatus configured to, with the aid of an antenna,generate and transmit radio-frequency signals as well as receiveradio-frequency signals and convert the information carried by suchreceived signals into a form usable by controller 103. Radiotransmitter/receiver 108 may be configured to transmit and/or receivevarious types of radio-frequency signals, including without limitation,cellular communications (e.g., 2G, 3G, 4G, LTE, etc.), short-rangewireless communications (e.g., BLUETOOTH), commercial radio signals,television signals, satellite radio signals (e.g., GPS), WirelessFidelity, etc.

A speaker 110 may be housed at least partially within enclosure 101 ormay be external to enclosure 101, may be communicatively coupled tocontroller 103, and may comprise any system, device, or apparatusconfigured to produce sound in response to electrical audio signalinput. In some embodiments, a speaker may comprise a dynamicloudspeaker, which employs a lightweight diaphragm mechanically coupledto a rigid frame via a flexible suspension that constrains a voice coilto move axially through a cylindrical magnetic gap. When an electricalsignal is applied to the voice coil, a magnetic field is created by theelectric current in the voice coil, making it a variable electromagnet.The coil and the driver's magnetic system interact, generating amechanical force that causes the coil (and thus, the attached cone) tomove back and forth, thereby reproducing sound under the control of theapplied electrical signal coming from the amplifier.

Force sensor 105 may be housed within enclosure 101, and may include anysuitable system, device, or apparatus for sensing a force, a pressure,or a touch (e.g., an interaction with a human finger) and generating anelectrical or electronic signal in response to such force, pressure, ortouch. In some embodiments, such electrical or electronic signal may bea function of a magnitude of the force, pressure, or touch applied tothe force sensor. In these and other embodiments, such electronic orelectrical signal may comprise a general purpose input/output signal(GPIO) associated with an input signal to which haptic feedback isgiven. Force sensor 105 may include, without limitation, a capacitivedisplacement sensor, an inductive force sensor (e.g., aresistive-inductive-capacitive sensor), a strain gauge, a piezoelectricforce sensor, force sensing resistor, piezoelectric force sensor, thinfilm force sensor, or a quantum tunneling composite-based force sensor.For purposes of clarity and exposition in this disclosure, the term“force” as used herein may refer not only to force, but to physicalquantities indicative of force or analogous to force, such as, but notlimited to, pressure and touch.

Linear resonant actuator 107 may be housed within enclosure 101, and mayinclude any suitable system, device, or apparatus for producing anoscillating mechanical force across a single axis. For example, in someembodiments, linear resonant actuator 107 may rely on an alternatingcurrent voltage to drive a voice coil pressed against a moving massconnected to a spring. When the voice coil is driven at the resonantfrequency of the spring, linear resonant actuator 107 may vibrate with aperceptible force. Thus, linear resonant actuator 107 may be useful inhaptic applications within a specific frequency range. While, for thepurposes of clarity and exposition, this disclosure is described inrelation to the use of linear resonant actuator 107, it is understoodthat any other type or types of vibrational actuators (e.g., eccentricrotating mass actuators) may be used in lieu of or in addition to linearresonant actuator 107. In addition, it is also understood that actuatorsarranged to produce an oscillating mechanical force across multiple axesmay be used in lieu of or in addition to linear resonant actuator 107.As described elsewhere in this disclosure, a linear resonant actuator107, based on a signal received from integrated haptic system 112, mayrender haptic feedback to a user of mobile device 102 for at least oneof mechanical button replacement and capacitive sensor feedback.

Integrated haptic system 112 may be housed within enclosure 101, may becommunicatively coupled to force sensor 105 and linear resonant actuator107, and may include any system, device, or apparatus configured toreceive a signal from force sensor 105 indicative of a force applied tomobile device 102 (e.g., a force applied by a human finger to a virtualbutton of mobile device 102) and generate an electronic signal fordriving linear resonant actuator 107 in response to the force applied tomobile device 102. Detail of an example integrated haptic system inaccordance with embodiments of the present disclosure is depicted inFIG. 2.

Resonant phase sensing system 113 may be housed within enclosure 101,may be communicatively coupled to force sensor 105 and linear resonantactuator 107, and may include any system, device, or apparatusconfigured to detect a displacement of a mechanical member (e.g.,mechanical member 305 depicted in FIGS. 3A and 3B, below) indicative ofa physical interaction (e.g., by a user of mobile device 102) with thehuman-machine interface of mobile device 102 (e.g., a force applied by ahuman finger to a virtual interface of mobile device 102). As describedin greater detail below, resonant phase sensing system 113 may detectdisplacement of such mechanical member by performing resonant phasesensing of a resistive-inductive-capacitive sensor for which animpedance (e.g., inductance, capacitance, and/or resistance) of theresistive-inductive-capacitive sensor changes in response todisplacement of the mechanical member. Thus, displacement of themechanical member may cause a change in an impedance of aresistive-inductive-capacitive sensor integral to resonant phase sensingsystem 113. Resonant phase sensing system 113 may also generate anelectronic signal to integrated haptic system 112 to which integratedhaptic system 112 may respond by driving linear resonant actuator 107 inresponse to a physical interaction associated with a human-machineinterface associated with the mechanical member. Detail of an exampleresonant phase sensing system 113 in accordance with embodiments of thepresent disclosure is depicted in greater detail below.

Although specific example components are depicted above in FIG. 1 asbeing integral to mobile device 102 (e.g., controller 103, memory 104,force sensor 105, microphone 106, radio transmitter/receiver 108,speakers(s) 110), a mobile device 102 in accordance with this disclosuremay comprise one or more components not specifically enumerated above.For example, although FIG. 1 depicts certain user interface components,mobile device 102 may include one or more other user interfacecomponents in addition to those depicted in FIG. 1 (including but notlimited to a keypad, a touch screen, and a display), thus allowing auser to interact with and/or otherwise manipulate mobile device 102 andits associated components.

FIG. 2 illustrates a block diagram of selected components of an exampleintegrated haptic system 112A, in accordance with embodiments of thepresent disclosure. In some embodiments, integrated haptic system 112Amay be used to implement integrated haptic system 112 of FIG. 1. Asshown in FIG. 2, integrated haptic system 112A may include a digitalsignal processor (DSP) 202, a memory 204, and an amplifier 206.

DSP 202 may include any system, device, or apparatus configured tointerpret and/or execute program instructions and/or process data. Insome embodiments, DSP 202 may interpret and/or execute programinstructions and/or process data stored in memory 204 and/or othercomputer-readable media accessible to DSP 202.

Memory 204 may be communicatively coupled to DSP 202, and may includeany system, device, or apparatus configured to retain programinstructions and/or data for a period of time (e.g., computer-readablemedia). Memory 204 may include random access memory (RAM), electricallyerasable programmable read-only memory (EEPROM), a Personal ComputerMemory Card International Association (PCMCIA) card, flash memory,magnetic storage, opto-magnetic storage, or any suitable selectionand/or array of volatile or non-volatile memory that retains data afterpower to mobile device 102 is turned off.

Amplifier 206 may be electrically coupled to DSP 202 and may compriseany suitable electronic system, device, or apparatus configured toincrease the power of an input signal VN (e.g., a time-varying voltageor current) to generate an output signal Vou-r. For example, amplifier206 may use electric power from a power supply (not explicitly shown) toincrease the amplitude of a signal. Amplifier 206 may include anysuitable amplifier class, including without limitation, a Class-Damplifier.

In operation, memory 204 may store one or more haptic playbackwaveforms. In some embodiments, each of the one or more haptic playbackwaveforms may define a haptic response a(t) as a desired acceleration ofa linear resonant actuator (e.g., linear resonant actuator 107) as afunction of time. DSP 202 may be configured to receive a force signalV_(SENSE) from resonant phase sensing system 113 indicative of forceapplied to force sensor 105. Either in response to receipt of forcesignal V_(SENSE) indicating a sensed force or independently of suchreceipt, DSP 202 may retrieve a haptic playback waveform from memory 204and process such haptic playback waveform to determine a processedhaptic playback signal V_(IN). In embodiments in which amplifier 206 isa Class D amplifier, processed haptic playback signal V_(IN) maycomprise a pulse-width modulated signal. In response to receipt of forcesignal V_(SENSE) indicating a sensed force, DSP 202 may cause processedhaptic playback signal V_(IN) to be output to amplifier 206, andamplifier 206 may amplify processed haptic playback signal V_(IN) togenerate a haptic output signal V_(OUT) for driving linear resonantactuator 107.

In some embodiments, integrated haptic system 112A may be formed on asingle integrated circuit, thus enabling lower latency than existingapproaches to haptic feedback control. By providing integrated hapticsystem 112A as part of a single monolithic integrated circuit, latenciesbetween various interfaces and system components of integrated hapticsystem 112A may be reduced or eliminated.

FIG. 3A illustrates a mechanical member 305 embodied as a metal plateseparated by a distance d from an inductive coil 302, in accordance withembodiments of the present disclosure. Mechanical member 305 maycomprise any suitable system, device, or apparatus which all or aportion thereof may displace, wherein such displacement affects anelectrical property (e.g., inductance, capacitance, etc.) of themechanical member 305 or another electrical component in electricalcommunication (e.g., via a mutual inductance) with mechanical member305.

FIG. 3B illustrates selected components of an inductive sensing system300 that may be implemented by force sensor 105 and/or resonant phasesensing system 113, in accordance with embodiments of the presentdisclosure. As shown in FIG. 3B, inductive sensing system 300 mayinclude mechanical member 305, modeled as a variable electricalresistance 304 and a variable electrical inductance 306, and may includeinductive coil 302 in physical proximity to mechanical member 305 suchthat inductive coil 302 has a mutual inductance with mechanical member305 defined by a variable coupling coefficient k. As shown in FIG. 3B,inductive coil 302 may be modeled as a variable electrical inductance308 and a variable electrical resistance 310.

In operation, as a current I flows through inductive coil 302, suchcurrent may induce a magnetic field which in turn may induce an eddycurrent inside mechanical member 305. When a force is applied to and/orremoved from mechanical member 305, which alters distance d betweenmechanical member 305 and inductive coil 302, the coupling coefficientk, variable electrical resistance 304, and/or variable electricalinductance 306 may also change in response to the change in distance.These changes in the various electrical parameters may, in turn, modifyan effective impedance Z_(L) of inductive coil 302.

FIG. 4 illustrates a diagram of selected components of an example system400 for performing resonant phase sensing, in accordance withembodiments of the present disclosure. In some embodiments, system 400may be used to implement resonant phase sensing system 113 of FIG. 1. Asshown in FIG. 4, system 400 may include a resistive-inductive-capacitivesensor 402 and a processing integrated circuit (IC) 412. In someembodiments, resistive-inductive-capacitive sensor 402 may implement allor a portion of force sensor 105 and processing integrated circuit (IC)412 may implement all or a portion of resonant phase sensing system 113.

As shown in FIG. 4, resistive-inductive-capacitive sensor 402 mayinclude mechanical member 305, inductive coil 302, a resistor 404, andcapacitor 406, wherein mechanical member 305 and inductive coil 302 havea variable coupling coefficient k. Although shown in FIG. 4 to bearranged in parallel with one another, it is understood that inductivecoil 302, resistor 404, and capacitor 406 may be arranged in any othersuitable manner that allows resistive-inductive-capacitive sensor 402 toact as a resonant tank. For example, in some embodiments, inductive coil302, resistor 404, and capacitor 406 may be arranged in series with oneanother. In some embodiments, resistor 404 may not be implemented with astand-alone resistor, but may instead be implemented by a parasiticresistance of inductive coil 302, a parasitic resistance of capacitor406, and/or any other suitable parasitic resistance.

Processing IC 412 may be communicatively coupled toresistive-inductive-capacitive sensor 402 and may comprise any suitablesystem, device, or apparatus configured to implement a measurementcircuit to measure phase information associated withresistive-inductive-capacitive sensor 402 and based on the phaseinformation, determine a displacement of mechanical member 305 relativeto resistive-inductive-capacitive sensor 402. Thus, processing IC 412may be configured to determine an occurrence of a physical interaction(e.g., press or release of a virtual button) associated with ahuman-machine interface associated with mechanical member 305 based onthe phase information.

As shown in FIG. 4, processing IC 412 may include a phase shifter 410, avoltage-to-current converter 408, a preamplifier 440, an intermediatefrequency mixer 442, a combiner 444, a programmable gain amplifier (PGA)414, a voltage-controlled oscillator (VCO) 416, a phase shifter 418, anamplitude and phase calculation block 431, a DSP 432, a low-pass filter434, a combiner 450, and a frequency and quality factor calculationengine 452. Processing IC 412 may also include a coherentincident/quadrature detector implemented with an incident channelcomprising a mixer 420, a low-pass filter 424, and an analog-to-digitalconverter (ADC) 428, and a quadrature channel comprising a mixer 422, alow-pass filter 426, and an ADC 430 such that processing IC 412 isconfigured to measure the phase information using the coherentincident/quadrature detector.

Phase shifter 410 may include any system, device, or apparatusconfigured to detect an oscillation signal generated by processing IC412 (as explained in greater detail below) and phase shift suchoscillation signal (e.g., by 45 degrees) such that at a normal operatingfrequency of system 400, an incident component of a sensor signal ϕgenerated by pre-amplifier 440 is approximately equal to a quadraturecomponent of sensor signal ϕ, so as to provide common mode noiserejection by a phase detector implemented by processing IC 412, asdescribed in greater detail below.

Voltage-to-current converter 408 may receive the phase shiftedoscillation signal from phase shifter 410, which may be a voltagesignal, convert the voltage signal to a corresponding current signal,and drive the current signal on resistive-inductive-capacitive sensor402 at a driving frequency with the phase-shifted oscillation signal inorder to generate sensor signal ϕ which may be processed by processingIC 412, as described in greater detail below. In some embodiments, adriving frequency of the phase-shifted oscillation signal may beselected based on a resonant frequency of resistive-inductive-capacitivesensor 402 (e.g., may be approximately equal to the resonant frequencyof resistive-inductive-capacitive sensor 402).

Preamplifier 440 may receive sensor signal ϕ and condition sensor signalϕ for frequency mixing, with mixer 442, to an intermediate frequency Δfcombined by combiner 444 with an oscillation frequency generated by VCO416, as described in greater detail below, wherein intermediatefrequency Δf is significantly less than the oscillation frequency. Insome embodiments, preamplifier 440, mixer 442, and combiner 444 may notbe present, in which case PGA 414 may receive sensor signal ϕ directlyfrom resistive-inductive-capacitive sensor 402. However, when present,preamplifier 440, mixer 442, and combiner 444 may allow for mixingsensor signal ϕ down to a lower intermediate frequency Δf which mayallow for lower-bandwidth and more efficient ADCs and/or which may allowfor minimization of phase and/or gain mismatches in the incident andquadrature paths of the phase detector of processing IC 412.

In operation, PGA 414 may further amplify sensor signal ϕ to conditionsensor signal ϕ for processing by the coherent incident/quadraturedetector. VCO 416 may generate an oscillation signal to be used as abasis for the signal driven by voltage-to-current converter 408, as wellas the oscillation signals used by mixers 420 and 422 to extractincident and quadrature components of amplified sensor signal ϕ. Asshown in FIG. 4, mixer 420 of the incident channel may use an unshiftedversion of the oscillation signal generated by VCO 416, while mixer 422of the quadrature channel may use a 90-degree shifted version of theoscillation signal phase shifted by phase shifter 418. As mentionedabove, the oscillation frequency of the oscillation signal generated byVCO 416 may be selected based on a resonant frequency ofresistive-inductive-capacitive sensor 402 (e.g., may be approximatelyequal to the resonant frequency of resistive-inductive-capacitive sensor402).

In the incident channel, mixer 420 may extract the incident component ofamplified sensor signal ϕ, low-pass filter 424 may filter out theoscillation signal mixed with the amplified sensor signal ϕ to generatea direct current (DC) incident component, and ADC 428 may convert suchDC incident component into an equivalent incident component digitalsignal for processing by amplitude and phase calculation block 431.Similarly, in the quadrature channel, mixer 422 may extract thequadrature component of amplified sensor signal ϕ, low-pass filter 426may filter out the phase-shifted oscillation signal mixed with theamplified sensor signal ϕ to generate a direct current (DC) quadraturecomponent, and ADC 430 may convert such DC quadrature component into anequivalent quadrature component digital signal for processing byamplitude and phase calculation block 431.

Amplitude and phase calculation block 431 may include any system,device, or apparatus configured to receive phase information comprisingthe incident component digital signal and the quadrature componentdigital signal and based thereon, extract amplitude and phaseinformation.

DSP 432 may include any system, device, or apparatus configured tointerpret and/or execute program instructions and/or process data. Inparticular, DSP 432 may receive the phase information and the amplitudeinformation generated by amplitude and phase calculation block 431 andbased thereon, determine a displacement of mechanical member 305relative to resistive-inductive-capacitive sensor 402, which may beindicative of an occurrence of a physical interaction (e.g., press orrelease of a virtual button or other interaction with a virtualinterface) associated with a human-machine interface associated withmechanical member 305 based on the phase information. DSP 432 may alsogenerate an output signal indicative of the displacement. In someembodiments, such output signal may comprise a control signal forcontrolling mechanical vibration of linear resonant actuator 107 inresponse to the displacement.

The phase information generated by amplitude and phase calculation block431 may be subtracted from a reference phase ϕ_(ref) by combiner 450 inorder to generate an error signal that may be received by low-passfilter 434. Low-pass filter 434 may low-pass filter the error signal,and such filtered error signal may be applied to VCO 416 to modify thefrequency of the oscillation signal generated by VCO 416, in order todrive sensor signal ϕ towards reference phase ϕ_(ref). As a result,sensor signal ϕ may comprise a transient decaying signal in response toa “press” of a virtual button (or other interaction with a virtualinterface) associated with system 400 as well as another transientdecaying signal in response to a subsequent “release” of the virtualbutton (or other interaction with a virtual interface). Accordingly,low-pass filter 434 in connection with VCO 416 may implement a feedbackcontrol loop that may track changes in operating parameters of system400 by modifying the driving frequency of VCO 416.

Frequency and quality factor calculation engine 452 may comprise anysystem, device, or apparatus configured to, as described in greaterdetail below, calculate a resonant frequency f₀ and/or a quality factorQ associated with resistive-inductive-capacitor sensor 402, such asthose caused by drift of physical parameters (e.g., aging, temperature,etc.) of force sensor 105, mechanical member 305, resonant phase sensingsystem 113, etc.

Although FIG. 4 depicts that, in some embodiments, frequency and qualityfactor calculation engine 452 is external to DSP 432, in someembodiments, functionality of frequency and quality factor calculationengine 452 may be implemented in whole or part by DSP 432.

Although the foregoing contemplates use of closed-loop feedback forsensing of displacement, the various embodiments represented by FIG. 4may be modified to implement an open-loop system for sensing ofdisplacement. In such an open-loop system, a processing IC may includeno feedback path from amplitude and phase calculation block 431 to VCO416 or variable phase shifter 418 and thus may also lack a feedbacklow-pass filter 434. Thus, a phase measurement may still be made bycomparing a change in phase to a reference phase value, but theoscillation frequency driven by VCO 416 may not be modified or the phaseshifted by variable phase shifter 418 may not be shifted.

Although the foregoing contemplates use of a coherentincident/quadrature detector as a phase detector for determining phaseinformation associated with resistive-inductive-capacitive sensor 402, aresonant phase sensing system 112 may perform phase detection and/orotherwise determine phase information associated withresistive-inductive-capacitive sensor 402 in any suitable manner,including, without limitation, using only one of the incident path orquadrature path to determine phase information.

In some embodiments, an incident/quadrature detector as disclosed hereinmay include one or more frequency translation stages that translate thesensor signal into direct-current signal directly or into anintermediate frequency signal and then into a direct-current signal. Anyof such frequency translation stages may be implemented either digitallyafter an analog-to-digital converter stage or in analog before ananalog-to-digital converter stage.

In addition, although the foregoing contemplates measuring changes inresistance and inductance in resistive-inductive-capacitive sensor 402caused by displacement of mechanical member 305, other embodiments mayoperate based on a principle that any change in impedance based ondisplacement of mechanical member 305 may be used to sense displacement.For example, in some embodiments, displacement of mechanical member 305may cause a change in a capacitance of resistive-inductive-capacitivesensor 402, such as if mechanical member 305 included a metal plateimplementing one of the capacitive plates of capacitor 406.

Although DSP 432 may be capable of processing phase information to makea binary determination of whether physical interaction associated with ahuman-machine interface associated with mechanical member 305 hasoccurred and/or ceased to occur, in some embodiments, DSP 432 mayquantify a duration of a displacement of mechanical member 305 to morethan one detection threshold, for example to detect different types ofphysical interactions (e.g., a short press of a virtual button versus along press of the virtual button). In these and other embodiments, DSP432 may quantify a magnitude of the displacement to more than onedetection threshold, for example to detect different types of physicalinteractions (e.g., a light press of a virtual button versus a quick andhard press of the virtual button).

Although FIG. 4 and the description thereof depicts particularembodiments of a resonant phase sensing system, other architectures forforce sensing may be used consistent with this disclosure, includingwithout limitation the various resonant phase sensing systemarchitectures described in U.S. patent application Ser. No. 16/267,079,filed Feb. 4, 2019. Thus, while frequency and quality factor calculationengine 452 is discussed herein in relation to operation in connectionwith a resonant phase sensing system, frequency and quality factorcalculation engine 452 may be used with any other suitable force sensingsystem.

Accordingly, using the systems and methods described above, aresistive-inductor-capacitive sensor is provided wherein part of theinductive component is exposed to the user in the form of a metal plateof a region of a chassis or enclosure (e.g., enclosure 101).

As such, displacements in the metal plate or enclosure may correlate tochanges in measured phase or amplitude.

As mentioned in the Background section of this application, for anactively-driven sensor system, it may be desirable that a signal driver(e.g., voltage-to-current converter 408) generate a signal at theresonant frequency of the sensor. Due to manufacturing designs andtolerances as well as environmental effects (e.g., temperature,humidity, movements in air gap over time, other changes in mechanicalstructures, etc.), resonant frequency f₀ and/or quality factor Q ofresistive-inductive-capacitive sensor 402 may be different from eachindividual sensor and may change over time. There are many reasons tooperate resistive-inductive-capacitive sensor 402 at or near resonantfrequency f₀, including without limitation:

-   -   As system 400 is a phase measurement system, the phase slope of        the sensor may be approximately linear and may have its highest        sensitivity close to resonant frequency f₀. Accordingly,        operating with a carrier frequency of the driving signal at or        near resonant frequency f₀ may optimize performance of system        400.    -   At frequencies away from resonant frequency f₀, a signal        amplitude developed across resistive-inductive-capacitive sensor        402 may be reduced, due to a smaller impedance presented by        resistive-inductive-capacitive sensor 402. This smaller signal        amplitude may lead to a decrease in a signal-to-noise-ratio        (SNR) of system 400.    -   Quality factor Q of resistive-inductive-capacitive sensor 402        may play a major role in translating the measured sensor signal        ϕ into force. Measuring a changing quality factor Q over time        may allow for system 400 to compensate for changes in a        phase-to-force translation. (Compensation for changing quality        factor Q is outside the scope of this disclosure).

Accordingly, as described in detail below, frequency and quality factorcalculation engine 452 may be configured to determine resonant frequencyf₀ and quality factor Q of resistive-inductive-capacitive sensor 402,and to adjust the drive frequency of a driving signal forresistive-inductive-capacitive sensor 402 (e.g., driven byvoltage-to-current converter 408 accordingly). As a result, system 400may measure relevant parameters, estimate changed values of the sensorparameters, and make some internal adjustments to “re-center” VCO 416and drive circuitry of system 400 to the optimal values forresistive-inductive-capacitive sensor 402.

The functionality of frequency and quality factor calculation engine 452may be illustrated with respect to FIG. 5, which illustrates an examplegraph of amplitude versus frequency for resistive-inductive-capacitivesensor 402, in accordance with embodiments of the present disclosure.FIG. 5 depicts three samples of amplitude A₀, A_(LO), and A_(HI), takenat resonant frequency f₀, a frequency f₀−f_(QLO), and a frequencyf₀+f_(QHI). Frequencies f₀−f_(QLO) and f₀+f_(QHI) may representfrequencies at which amplitudes A_(LO) and A_(HI) are three decibelslower than amplitude A₀ at resonant frequency f₀

$\left( {{e.g.},{A_{L0} = {A_{HI} = {\frac{\sqrt{2}}{2}{A_{0}.}}}}} \right.$

FIG. 5 also depicts a slope mm between the sample of amplitude A_(LO) atfrequency f₀−f_(QLO) and the sample of amplitude A₀ at resonantfrequency f₀, and further depicts a slope m_(HI) between the sample ofamplitude A₀ at resonant frequency f₀ and sample of amplitude A_(HI) atfrequency f₀+f_(QHI). Slope m_(LO) and slope min may be given as:

${m_{LO} = \frac{A_{0} - A_{LO}}{f_{QLO}}},{m_{HI} = \frac{A_{HI} - A_{0}}{f_{Q{HI}}}}$

If perfect symmetry is assumed for amplitude versus frequency aboutresonant frequency f₀, then m_(LO)+m_(HI)=0, although such assumptionmay not be viable for a very low quality factor Q.

Taking actual values for slopes m_(LO) and m_(HI) from sensor modelsacross multiple quality factors Q and resonant frequencies f₀, slopesm_(LO) and m_(HI) may be modeled in a linear equation as a function ofquality factor Q as follows:

f ₀ Q(m _(LO) +m _(HI))≈A _(peak)(m _(Q) Q+b _(Q))  (1)

wherein A_(peak) is a peak amplitude of the curve, m_(Q) is a slope ofthe linear equation, and b_(Q) is the y-intercept of the linearequation. Accordingly, if slopes m_(LO) and m_(HI) are scales withresonant frequency f₀ and quality factor Q, a result may be producedthat is approximately linear with quality factor Q. Thus, frequency andquality factor calculation engine 452 may use linear curve fitting withsensor model data to find the slope m_(Q) and y-intercept b_(Q) of thelinear model.

Once solving the linear model, frequency and quality factor calculationengine 452 may formulate equations for updating an estimate of resonantfrequency f₀ based on the relationships above. In other words, updatedslopes m_(LO) and m_(HI) may be given by:

${m_{LO} = \frac{\left( {A_{0} + {\Delta A_{0}}} \right) - A_{LO}}{{\Delta f_{0}} + f_{QLO}}},{m_{HI} = \frac{\left( {A_{0} + {\Delta A_{0}}} \right) - A_{HI}}{{\Delta f_{0}} - f_{Q{HI}}}}$

and resonant frequency f₀ may be updated by substituting updated slopesm_(LO) and m_(HI) into the linear model:

${\Delta f_{0}} = \frac{\begin{matrix}\begin{matrix}{{f_{Q{HI}}\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{LO}} \right\rbrack} -} \\{{f_{QLO}\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{HI}} \right\rbrack} -}\end{matrix} \\{\frac{f_{Q{HI}}f_{QLO}}{f_{0}}{A_{0}\left( {m_{Q} + {b_{Q}\frac{f_{Q}}{f_{0}}}} \right)}}\end{matrix}}{\begin{matrix}\begin{matrix}{\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{LO}} \right\rbrack +} \\{\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{HI}} \right\rbrack +}\end{matrix} \\{\frac{\left( {f_{QHI} - f_{QLO}} \right)}{f_{0}}{A_{0}\left( {m_{Q} + {b_{Q}\frac{f_{Q}}{f_{0}}}} \right)}}\end{matrix}}$

where change in amplitude A₀ may be used to dampen a response fromringing between sampling iterations.

As mentioned above, to implement the estimation of resonant frequency f₀and quality factor Q of resistive-inductive-capacitive sensor 402 asdescribed herein, frequency and quality factor calculation engine 452may take as few as three measurements of amplitude at three frequencies,as follows:

A _(LO)(f _(est) −f _(QLO)),A ₀(f _(est)),A _(HI)(f _(est) +f _(QHI))

Once the estimation has converged, sample measurement A₀(f_(est)) mayrepresent the amplitude at resonant frequency f₀, and samplemeasurements A_(LO)(f_(est)−f_(QLO)) and A_(HI)(f_(est)+f_(QHI)) mayrepresent frequencies at which amplitude is 3 decibels less thanamplitude A₀ at resonant frequency f₀.

Quality factor Q may then be given by:

${Q = \frac{f_{0}}{f_{Q}}},{f_{Q} = {f_{Q{HI}} + f_{QLO}}}$

Given a typical response of resistive-inductive-capacitive sensor 402,it may determine a “direction” of a location of actual resonantfrequency f₀ based on a slope between A_(LO)(f_(est)−f_(QLO)) andA₀(f_(est)) and a slope between A_(HI)(f_(est)+f_(QHI)) and A₀(f_(est)).For example, referring to FIGS. 6A-6C, which illustrate additionalexample graphs of amplitude versus frequency forresistive-inductive-capacitive sensor 402 in different possibleamplitude response regions, in accordance with embodiments of thepresent disclosure:

-   -   When m_(LO)>0 and m_(HI)>0, resonant frequency        f₀>f_(est)+f_(QHI)    -   When m_(LO)>0 and m_(HI)<0, f_(est)−f_(QLO)<f₀<f_(est)+f_(QHI)    -   When m_(LO)>0 and m_(HI)>0, resonant frequency        f₀<f_(est)−f_(QLO)

Further, it may be evident from FIG. 5 that if m_(LO)>0 and m_(HI)<0,the sum of m_(LO) and m_(HI) should approach zero as estimated frequencyf_(est) approaches resonant frequency f₀. However, as also mentionedabove, assuming m_(LO)+m_(HI)=0 at resonance may be a correct assumptionfor estimating resonant frequency f₀ for sensors with lower values ofquality factor Q (e.g., Q<˜6). To that end, FIG. 7 illustrates anexample graph of the sum m_(LO)+m_(HI) versus quality factor Q for asingle resonant frequency, in accordance with embodiments of the presentdisclosure. The curve shown in FIG. 7 may be modeled as:

$\left. {\frac{f_{0}{Q\left( {m_{LO} + m_{HI}} \right)}}{A_{peak}} \approx {{m_{Q}Q} + b_{Q}}}\rightarrow{{m_{LO} + m_{HI}} \approx {\frac{A_{peak}}{f_{0}}\left( {m_{Q} + \frac{b_{Q}}{Q}} \right)}} \right.$

and thus, Q(m_(LO)+m_(HI)) may be modeled as approximately linear with aslope of m_(Q) and a y-intercept of bQ, as shown in FIG. 8.

To estimate resonant frequency f₀ and quality factor Q, samplemeasurements A₀(f_(est)), A_(LO)(f_(est)−f_(QLO)), andA_(LO)(f_(est)+f_(QHI)) may iteratively be taken, with estimatedfrequency f_(est) updated for each iteration, eventually converging withresonant frequency f₀.

For example, for the case in which mu)>0 and m_(HI)<0, estimatedfrequency fa may be updated by substituting f₀=f_(est) and

$Q = \frac{f_{est}}{f_{Q}}$

into the linear model equation (1) from above, which yields:

$\begin{matrix}{{\frac{f_{est}^{2}}{f_{Q}}\left( {m_{LO} + m_{HI}} \right)} = {A_{0}\left( {{m_{Q}\frac{f_{est}}{f_{Q}}} + b_{Q}} \right)}} & (2)\end{matrix}$

wherein A₀ is substituted for peak amplitude A_(peak).

Further, slopes m_(LO) and m_(HI) may be updated in accordance with:

${m_{LO} = \frac{\left( {A_{0} + {\Delta A_{0}}} \right) - A_{LO}}{{\Delta f_{est}} + f_{QLO}}},{m_{HI} = \frac{\left( {A_{0} + {\Delta A_{0}}} \right) - A_{HI}}{{\Delta f_{est}} - f_{Q{HI}}}}$

and substituted into equation (2), which yields:

$\begin{matrix}{{\frac{f_{est}^{2}}{f_{Q}}\left\lbrack {\frac{\begin{matrix}{\left( {A_{0} + {\Delta A_{0}}} \right) -} \\A_{LO}\end{matrix}}{{\Delta f_{est}} + f_{QLO}} + \frac{\left( {A_{0} + {\Delta A_{0}}} \right) - A_{HI}}{{\Delta f_{est}} - f_{Q{HI}}}} \right\rbrack} = {A_{0}\left( {{m_{Q}\frac{f_{est}}{f_{Q}}} + b_{Q}} \right)}} & (3)\end{matrix}$

By collecting like terms from equation (3) and assuming Δf_(est) ²≈0,frequency and quality factor calculation engine 452 may solve for adelta update Δ_(fest) in estimated frequency f_(est) as:

${\Delta f_{est}} = \frac{\begin{matrix}\begin{matrix}{{f_{Q{HI}}\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{LO}} \right\rbrack} -} \\{{f_{QLO}\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{HI}} \right\rbrack} -}\end{matrix} \\{\frac{f_{Q{HI}}f_{QLO}}{f_{est}}{A_{0}\left( {m_{Q} + {b_{Q}\frac{f_{Q}}{f_{est}}}} \right)}}\end{matrix}}{\begin{matrix}\begin{matrix}{\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{LO}} \right\rbrack +} \\{\left\lbrack {\left( {A_{0} + {\Delta A_{0}}} \right) - A_{HI}} \right\rbrack +}\end{matrix} \\{\frac{\left( {f_{QHI} - f_{QLO}} \right)}{f_{est}}{A_{0}\left( {m_{Q} + {b_{Q}\frac{f_{Q}}{f_{est}}}} \right)}}\end{matrix}}$

A change ΔA₀ in amplitude may be dampened by the relation asΔA₀=λ|A_(HI)−A_(LO)|, where λ is a parameter between 0 and 1 that maycontrol an amount of dampening.

After updating estimated frequency f_(est) by delta update Δ_(fest),frequency and quality factor calculation engine 452 may update sum f_(Q)of frequencies f_(QLO) and f_(QHI), with the goal of updatingfrequencies f_(QLO) and f_(QHI) to the points at which

$A_{LO} = {A_{HI} = {\frac{\sqrt{2}}{2}{A_{0}.}}}$

Assuming perfect symmetry about resonant frequency f₀:

${m_{LO} + m_{HI}} = {\left. 0\rightarrow{\frac{A_{0} - A_{LO}}{{\Delta f_{0}} + f_{QLO}} + \frac{A_{0} - A_{HI}}{{\Delta f_{0}} - f_{QHI}}} \right. = {0\mspace{14mu}{and}\text{:}}}$${\Delta f_{est}} = \frac{{f_{QHI}\left( {A_{0} - A_{LO}} \right)} - {f_{QLO}\left( {A_{0} - A_{HI}} \right)}}{\left( {A_{0} - A_{LO}} \right) + \left( {A_{0} - A_{HI}} \right)}$

Thus, frequency f_(QLO) may be updated by a delta frequency Δf_(QLO) inaccordance with:

$\mspace{20mu}{{{\frac{\sqrt{2}}{2}A_{0}} - A_{LO}} = {{m_{LO}\left( {{\Delta f_{est}} - {\Delta f_{QLO}}} \right)}\mspace{14mu}{and}\text{:}}}$$m_{LO} = {\left. \frac{A_{0} - A_{LO}}{{\Delta f_{est}} + f_{QLO}}\rightarrow m_{LO} \right. = {\left. \frac{A_{0} - A_{LO}}{\left\lbrack \frac{\begin{matrix}{{f_{QHI}\left( {A_{0} - A_{LO}} \right)} -} \\{f_{QLO}\left( {A_{0} - A_{HI}} \right)}\end{matrix}}{\begin{matrix}{\left( {A_{0} - A_{LO}} \right) +} \\\left( {A_{0} - A_{HI}} \right)\end{matrix}} \right\rbrack + f_{QLO}}\rightarrow m_{LO} \right. = \frac{\begin{matrix}{\left( {A_{0} - A_{LO}} \right) +} \\\left( {A_{0} - A_{HI}} \right)\end{matrix}}{f_{QHI} + f_{QLO}}}}$

By substitution of slope m_(LO) and delta frequency Δf_(est) to solvefor delta frequency Δf_(QLO):

${\Delta f_{QLO}} = {{\Delta f_{est}} - \frac{\left( {f_{QHI} + f_{QLO}} \right)\left( {{\frac{\sqrt{2}}{2}A_{0}} - A_{LO}} \right)}{\left( {A_{0} - A_{LO}} \right) + \left( {A_{0} - A_{HI}} \right)}}$

Similarly, frequency f_(QHI) may be updated by a delta frequencyΔf_(QHI) in accordance with:

$\mspace{20mu}{{{\frac{\sqrt{2}}{2}A_{0}} - A_{HI}} = {{{m_{HI}\left( {{\Delta f_{est}} + {\Delta\; f_{QHI}}} \right)}\mspace{14mu}{{and}:m_{HI}}} = {\left. \frac{A_{0} - A_{HI}}{{\Delta f_{est}} - f_{QHI}}\rightarrow m_{HI} \right. = {\left. \frac{A_{0} - A_{HI}}{\left\lbrack \frac{\begin{matrix}{{f_{QHI}\left( {A_{0} - A_{LO}} \right)} -} \\{f_{QLO}\left( {A_{0} - A_{HI}} \right)}\end{matrix}}{\begin{matrix}{\left( {A_{0} - A_{LO}} \right) +} \\\left( {A_{0} - A_{HI}} \right)\end{matrix}} \right\rbrack - f_{QHI}}\rightarrow m_{HI} \right. = \frac{- \begin{bmatrix}{\left( {A_{0} - A_{LO}} \right) +} \\\left( {A_{0} - A_{HI}} \right)\end{bmatrix}}{f_{QHI} + f_{QLO}}}}}}$

By substitution of slope m_(HI) and delta frequency Δf_(est) to solvefor delta frequency Δf_(QHI):

${\Delta f_{{QH}\; I}} = {{{- \Delta}f_{est}} - \frac{\left( {f_{QHI} + f_{QLO}} \right)\left( {{\frac{\sqrt{2}}{2}A_{0}} - A_{HI}} \right)}{\left( {A_{0} - A_{LO}} \right) + \left( {A_{0} - A_{HI}} \right)}}$

As another example, for the case in which m_(HI)>0 as shown in FIG. 9,it may be safe to assume that resonant frequency f₀ is higher thanestimated frequency f_(est). In such case, frequency and quality factorcalculation engine 452 may update estimated frequency f_(est) by firstcalculating a new slope m_(LO_AVG) by taking the average of slope m_(LO)between sample points (f_(est)−f_(QLO), A_(LO)) and (f_(est), A₀) andslope mc between sample points (f_(est)−f_(QLO), A_(LO)) and(f_(est)+f_(QHI), A_(HI)). A line equation with this average slopem_(LO_AVG) may be used by frequency and quality factor calculationengine 452 to find a new estimated frequency at an amplitude between A₀and A_(HI), for example at a point (f_(est)+Δf_(est), 0.5(A₀+A_(HI))) onthe amplitude versus frequency curve, resulting in a new frequencyestimation between the existing estimated frequency f_(est) andfrequency f_(est)+f_(QHI).

To further illustrate, under such approach, frequency and quality factorcalculation engine 452 may calculate average slope m_(LO_AVG) as:

$m_{LO_{AVG}} = {{\frac{1}{2}\left\lbrack {m_{LO} + m_{C}} \right\rbrack} = {{\frac{1}{2}\left\lbrack {\frac{A_{0} - A_{LO}}{f_{QLO}} + \frac{A_{HI} - A_{LO}}{f_{QHI} + f_{QLO}}} \right\rbrack} = {\frac{1}{2}\left\lbrack \frac{\begin{matrix}{{f_{QLO}\left( {A_{HI} - A_{LO}} \right)} +} \\{\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{0} - A_{LO}} \right)}\end{matrix}}{f_{QLO}\left( {f_{QHI} + f_{QLO}} \right)} \right\rbrack}}}$

An equation of a line with slope m_(LO_AVG) through points(f_(est)−f_(QLO), A_(LO)) and point (f_(est)+Δf_(est), 0.5(A₀+A_(HI)))may be given by:

${\frac{A_{HI} + A_{0}}{2} - A_{LO}} = {m_{LO_{AVG}}\left\lbrack {\left( {f_{est} + {\Delta f_{est}}} \right) - \left( {f_{est} - f_{QLO}} \right)} \right\rbrack}$

Substituting the equation for slope m_(LO_AVG) into the foregoingequation and solving for delta frequency Δf_(est):

${\Delta f_{est}} = {\frac{{f_{QLO}\left( {f_{QHI} + f_{QLO}} \right)}\left( {A_{HI} + A_{0} - {2A_{LO}}} \right)}{{f_{QLO}\left( {A_{HI} - A_{LO}} \right)} + {\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{0} - A_{LO}} \right)}} - f_{QLO}}$

As shown in FIG. 10, to update frequency f_(QLO), the line describedabove with slope m_(LO_AVG) may be evaluated at a new frequency forfrequency f_(QLO) at which amplitude is

$\frac{\sqrt{2}}{2}{\frac{\left( {A_{0} + A_{HI}} \right)}{2}.}$

Further, frequency f_(QHI) may be updated such that frequency f_(QLO)and frequency f_(QHI) are symmetrical around the new estimated frequencyf_(est)+Δf_(est).

To further illustrate, an equation of a line may be given by:

${\left( {\frac{\sqrt{2}}{2} - 1} \right)\frac{A_{HI} + A_{0}}{2}} = {m_{LO_{AVG}}\left\lbrack {\left( {f_{est} + {\Delta f_{est}}} \right) - \left( {f_{QLO} + {\Delta f_{QLO}}} \right) - \left( {f_{est} + {\Delta f_{est}}} \right)} \right\rbrack}$

Substituting the equation for slope m_(LO_AVG) into the foregoingequation and solving for delta frequency Δf_(QLO):

${\Delta f_{QLO}} = {\frac{{f_{QLO}\left( {f_{QHI} + f_{QLO}} \right)}\left( {1 - \frac{\sqrt{2}}{2}} \right)\left( {A_{0} + A_{HI}} \right)}{{f_{QLO}\left( {A_{HI} - A_{LO}} \right)} + {\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{0} - A_{LO}} \right)}} - f_{QLO}}$

Similarly, solving for delta frequency Δf_(QLO):

${\Delta f_{QHI}} = {\frac{{f_{QLO}\left( {f_{QHI} + f_{QLO}} \right)}\left( {1 - \frac{\sqrt{2}}{2}} \right)\left( {A_{0} + A_{HI}} \right)}{{f_{QLO}\left( {A_{HI} - A_{LO}} \right)} + {\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{0} - A_{LO}} \right)}} - f_{QHI}}$

As a further example, for the case in which m_(LO)<0 as shown in FIG.11, it may be safe to assume that resonant frequency f₀ is lower thanestimated frequency f_(est). In such case, frequency and quality factorcalculation engine 452 may update estimated frequency f_(est) by firstcalculating a new slope m_(HI_AVG) by taking the average of slope mmbetween sample points (f_(est)+f_(QHI), A_(HI)) and (f_(est), A₀) andslope mc between sample points (f_(est)−f_(QLO), A_(LO)) and(f_(est)+f_(QHI), A_(HI)). A line equation with this average slopem_(HI_AVG) may be used by frequency and quality factor calculationengine 452 to find a new estimated frequency at an amplitude between A₀and A_(LO), for example at a point (f_(est)+Δf_(est), 0.5(A₀+A_(LO))) onthe amplitude versus frequency curve, resulting in a new frequencyestimation between the existing estimated frequency f_(est) andfrequency f_(est)−f_(QLO).

To further illustrate, under such approach, frequency and quality factorcalculation engine 452 may calculate average slope m_(HI_AVG) as:

$m_{{HI}_{AVG}} = {{\frac{1}{2}\left\lbrack {m_{HI} + m_{C}} \right\rbrack} = {{\frac{1}{2}\left\lbrack {\frac{A_{HI} - A_{0}}{f_{QHI}} + \frac{A_{HI} - A_{LO}}{f_{QHI} + f_{QLO}}} \right\rbrack} = {\frac{1}{2}\left\lbrack \frac{\begin{matrix}{{f_{QHI}\left( {A_{HI} - A_{LO}} \right)} +} \\{\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{HI} - A_{0}} \right)}\end{matrix}}{f_{QHI}\left( {f_{QHI} + f_{QLO}} \right)} \right\rbrack}}}$

An equation of a line with slope m_(HI_AVG) through points(f_(est)+f_(QHI), A_(HI)) and point (f_(est)+Δf_(est), 0.5(A₀+A_(LO)))may be given by:

${\frac{A_{LO} + A_{0}}{2} - A_{HI}} = {m_{{HI}_{AVG}}\left\lbrack {\left( {f_{est} + {\Delta f_{est}}} \right) - \left( {f_{est} + f_{QHI}} \right)} \right\rbrack}$

Substituting the equation for slope m_(HI_AVG) into the foregoingequation and solving for delta frequency Δf_(est):

${\Delta f_{est}} = {\frac{{f_{QHI}\left( {f_{QHI} + f_{QLO}} \right)}\left( {A_{LO} + A_{0} - {2A_{HI}}} \right)}{{f_{QHI}\left( {A_{HI} - A_{LO}} \right)} + {\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{HI} - A_{0}} \right)}} + f_{QHI}}$

As shown in FIG. 12, to update frequency f_(QHI), the line describedabove with slope m_(HI_AVG) may be evaluated at a new frequency forfrequency f_(QHI) at which amplitude is

$\frac{\sqrt{2}}{2}{\frac{\left( {A_{0} + A_{LO}} \right)}{2}.}$

Further, frequency f_(QLO) may be updated such that frequency f_(QLO)and frequency f_(QHI) are symmetrical around the new estimated frequencyf_(est)+Δf_(est).

To further illustrate, an equation of a line may be given by:

${\left( {\frac{\sqrt{2}}{2} - 1} \right)\frac{A_{LO} + A_{0}}{2}} = {m_{{HI}_{AVG}}\left\lbrack {\left( {f_{est} + {\Delta f_{est}}} \right) + \left( {f_{QHI} + {\Delta f_{QHI}}} \right) - \left( {f_{0} + {\Delta f_{0}}} \right)} \right\rbrack}$

Substituting the equation for slope m_(HI_AVG) into the foregoingequation and solving for delta frequency Δf_(QHI):

${\Delta f_{QHI}} = {\frac{{f_{QHI}\left( {f_{QHI} + f_{QLO}} \right)}\left( {\frac{\sqrt{2}}{2} - 1} \right)\left( {A_{LO} + A_{0}} \right)}{{f_{QHI}\left( {A_{HI} - A_{LO}} \right)} + {\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{HI} - A_{0}} \right)}} - f_{QHI}}$

Similarly, solving for delta frequency Δf_(QLO):

${\Delta f_{QLO}} = {\frac{{f_{QHI}\left( {f_{QHI} + f_{QLO}} \right)}\left( {\frac{\sqrt{2}}{2} - 1} \right)\left( {A_{LO} + A_{0}} \right)}{{f_{QHI}\left( {A_{HI} - A_{LO}} \right)} + {\left( {f_{QHI} + f_{QLO}} \right)\left( {A_{HI} - A_{0}} \right)}} - f_{QLO}}$

To ultimately estimate resonant frequency f₀, frequency and qualityfactor calculation engine 452 may iteratively perform theabove-described steps of sampling amplitude versus frequency at as fewas three points including an estimated resonant frequency f_(est),updating the frequencies (including estimated resonant frequencyf_(est)) based on the measurements, and repeating these steps untilestimated resonant frequency f_(est) converges (e.g., successive changesbetween estimated resonant frequency f_(est) fall below a thresholdvalue).

As used herein, when two or more elements are referred to as “coupled”to one another, such term indicates that such two or more elements arein electronic communication or mechanical communication, as applicable,whether connected indirectly or directly, with or without interveningelements.

This disclosure encompasses all changes, substitutions, variations,alterations, and modifications to the example embodiments herein that aperson having ordinary skill in the art would comprehend. Similarly,where appropriate, the appended claims encompass all changes,substitutions, variations, alterations, and modifications to the exampleembodiments herein that a person having ordinary skill in the art wouldcomprehend. Moreover, reference in the appended claims to an apparatusor system or a component of an apparatus or system being adapted to,arranged to, capable of, configured to, enabled to, operable to, oroperative to perform a particular function encompasses that apparatus,system, or component, whether or not it or that particular function isactivated, turned on, or unlocked, as long as that apparatus, system, orcomponent is so adapted, arranged, capable, configured, enabled,operable, or operative. Accordingly, modifications, additions, oromissions may be made to the systems, apparatuses, and methods describedherein without departing from the scope of the disclosure. For example,the components of the systems and apparatuses may be integrated orseparated. Moreover, the operations of the systems and apparatusesdisclosed herein may be performed by more, fewer, or other componentsand the methods described may include more, fewer, or other steps.Additionally, steps may be performed in any suitable order. As used inthis document, “each” refers to each member of a set or each member of asubset of a set.

Although exemplary embodiments are illustrated in the figures anddescribed below, the principles of the present disclosure may beimplemented using any number of techniques, whether currently known ornot. The present disclosure should in no way be limited to the exemplaryimplementations and techniques illustrated in the drawings and describedabove.

Unless otherwise specifically noted, articles depicted in the drawingsare not necessarily drawn to scale.

All examples and conditional language recited herein are intended forpedagogical objects to aid the reader in understanding the disclosureand the concepts contributed by the inventor to furthering the art, andare construed as being without limitation to such specifically recitedexamples and conditions. Although embodiments of the present disclosurehave been described in detail, it should be understood that variouschanges, substitutions, and alterations could be made hereto withoutdeparting from the spirit and scope of the disclosure.

Although specific advantages have been enumerated above, variousembodiments may include some, none, or all of the enumerated advantages.Additionally, other technical advantages may become readily apparent toone of ordinary skill in the art after review of the foregoing figuresand description.

To aid the Patent Office and any readers of any patent issued on thisapplication in interpreting the claims appended hereto, applicants wishto note that they do not intend any of the appended claims or claimelements to invoke 35 U.S.C. § 112(f) unless the words “means for” or“step for” are explicitly used in the particular claim.

What is claimed is:
 1. A method for determining sensor parameters of anactively-driven sensor system, comprising: obtaining as few as threesamples of a measured physical quantity versus frequency for theactively-driven sensor system; performing a refinement operation toprovide a refined version of the sensor parameters based on the as fewas three samples and based on a linear model of an asymmetry betweenslopes of the measured physical quantity versus frequency between pairsof the as few as three samples; iteratively repeating the refinementoperation until the difference between successive refined versions ofthe sensor parameters is below a defined threshold; and outputting therefined sensor parameters as updated sensor parameters for theactively-driven sensor system.
 2. The method of claim 1, wherein thesensor parameters comprise one or more of a resonant frequency and aquality factor of the actively-driven sensor system.
 3. The method ofclaim 1, wherein the measured physical quantity comprises an amplitudeassociated with the actively-driven sensor system.
 4. The method ofclaim 1, wherein the as few as three samples are obtained at: a firstfrequency estimating a resonant frequency of the actively-driven sensorsystem; a second frequency lower than the first frequency; and a thirdfrequency higher than the first frequency.
 5. The method of claim 4,wherein a first difference between the third frequency and the firstfrequency is approximately equal to a second difference between thefirst frequency and the second frequency.
 6. The method of claim 5,wherein slopes of the measured physical quantity versus frequencybetween pairs of the as few as three samples comprise: a first slopebetween a first sample obtained at the first frequency and a secondsample obtained at the second frequency; and a second slope between thefirst sample and a third sample obtained at the third frequency.
 7. Themethod of claim 6, wherein the refinement operation comprises, when thefirst slope is positive and the second slope is negative: increasing thefirst frequency for a subsequent iteration if a magnitude of the firstslope is greater than a magnitude of the second slope; and decreasingthe first frequency for the subsequent iteration if a magnitude of thefirst slope is lesser than a magnitude of the second slope.
 8. Themethod of claim 6, wherein the refined version of the sensor parametersis based on the first slope and the second slope.
 9. The method of claim6, wherein the refinement operation comprises, when the second slope ispositive, increasing the first frequency for a subsequent iteration. 10.The method of claim 9, wherein the refinement operation comprisesincreasing the first frequency to a frequency between the firstfrequency and the third frequency.
 11. The method of claim 6, whereinthe refinement operation comprises, when the first slope is negative,increasing the first frequency for a subsequent iteration.
 12. Themethod of claim 11, wherein the refinement operation comprisesdecreasing the first frequency to a frequency between the firstfrequency and the second frequency.
 13. The method of claim 4, whereinthe second frequency and the third frequency each estimate frequenciesat which an amplitude of the physical quantity is three decibels lowerthan the amplitude at the resonant frequency.
 14. The method of claim 1,wherein the as few as three samples of the measured physical quantityare based on a previous iteration of the refinement operation.
 15. Themethod of claim 1, wherein the actively-driven sensor system comprises aforce sensor.
 16. The method of claim 15, wherein the force sensor isconfigured to sense a force associated with a human interaction with avirtual button.
 17. The method of claim 16, wherein the force sensorcomprises one of a capacitive displacement sensor, an inductive forcesensor, a resistive-inductive-capacitive sensor, a strain gauge, apiezoelectric force sensor, a force sensing resistor, a piezoelectricforce sensor, a thin film force sensor, or a quantum tunnelingcomposite-based force sensor.
 18. The method of claim 1, wherein theactively-driven sensor system comprises a resistive-inductive-capacitivesensor.
 19. A system comprising: an actively-driven sensor; and ameasurement circuit communicatively coupled to the actively-drivensensor and configured to: obtain as few as three samples of a measuredphysical quantity versus frequency for the actively-driven sensorsystem; perform a refinement operation to provide a refined version ofthe sensor parameters based on the as few as three samples and based ona linear model of an asymmetry between slopes of the measured physicalquantity versus frequency between pairs of the as few as three samples;iteratively repeat the refinement operation until the difference betweensuccessive refined versions of the sensor parameters is below a definedthreshold; and output the refined sensor parameters as updated sensorparameters for the actively-driven sensor system.
 20. The system ofclaim 19, wherein the sensor parameters comprise one or more of aresonant frequency and a quality factor of the actively-driven sensorsystem.
 21. The system of claim 19, wherein the measured physicalquantity comprises an amplitude associated with the actively-drivensensor system.
 22. The system of claim 19, wherein the as few as threesamples are obtained at: a first frequency estimating a resonantfrequency of the actively-driven sensor system; a second frequency lowerthan the first frequency; and a third frequency higher than the firstfrequency.
 23. The system of claim 22, wherein a first differencebetween the third frequency and the first frequency is approximatelyequal to a second difference between the first frequency and the secondfrequency.
 24. The system of claim 23, wherein slopes of the measuredphysical quantity versus frequency between pairs of the as few as threesamples comprise: a first slope between a first sample obtained at thefirst frequency and a second sample obtained at the second frequency;and a second slope between the first sample and a third sample obtainedat the third frequency.
 25. The system of claim 24, wherein therefinement operation comprises, when the first slope is positive and thesecond slope is negative: increasing the first frequency for asubsequent iteration if a magnitude of the first slope is greater than amagnitude of the second slope; and decreasing the first frequency forthe subsequent iteration if a magnitude of the first slope is lesserthan a magnitude of the second slope.
 26. The system of claim 24,wherein the refined version of the sensor parameters is based on thefirst slope and the second slope.
 27. The system of claim 24, whereinthe refinement operation comprises, when the second slope is positive,increasing the first frequency for a subsequent iteration.
 28. Thesystem of claim 27, wherein the refinement operation comprisesincreasing the first frequency to a frequency between the firstfrequency and the third frequency.
 29. The system of claim 24, whereinthe refinement operation comprises, when the first slope is negative,increasing the first frequency for a subsequent iteration.
 30. Thesystem of claim 29, wherein the refinement operation comprisesdecreasing the first frequency to a frequency between the firstfrequency and the second frequency.
 31. The system of claim 22, whereinthe second frequency and the third frequency each estimate frequenciesat which an amplitude of the physical quantity is three decibels lowerthan the amplitude at the resonant frequency.
 32. The system of claim19, wherein the as few as three samples of the measured physicalquantity are based on a previous iteration of the refinement operation.33. The system of claim 19, wherein the actively-driven sensor systemcomprises a force sensor.
 34. The system of claim 33, wherein the forcesensor is configured to sense a force associated with a humaninteraction with a virtual button.
 35. The system of claim 34, whereinthe force sensor comprises one of a capacitive displacement sensor, aninductive force sensor, a resistive-inductive-capacitive sensor, astrain gauge, a piezoelectric force sensor, a force sensing resistor, apiezoelectric force sensor, a thin film force sensor, or a quantumtunneling composite-based force sensor.
 36. The system of claim 19,wherein the actively-driven sensor system comprises aresistive-inductive-capacitive sensor.